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Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at O(G^{4}).

Zvi Bern1, Julio Parra-Martinez2, Radu Roiban3

  • 1Mani L. Bhaumik Institute for Theoretical Physics, University of California at Los Angeles, Los Angeles, California 90095, USA.

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|May 6, 2022
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Summary
This summary is machine-generated.

We calculated conservative two-body scattering dynamics to the fourth post-Minkowskian order, including radiative effects. This research advances gravitational wave physics and our understanding of general relativity using modern scattering amplitude techniques.

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Area of Science:

  • Gravitational physics
  • General relativity
  • High-energy theoretical physics

Background:

  • Accurate modeling of binary black hole mergers is crucial for gravitational wave astronomy.
  • Previous calculations of gravitational dynamics have been limited in precision.
  • Understanding radiative effects, like the tail effect, is essential for precise predictions.

Purpose of the Study:

  • To compute conservative two-body scattering dynamics at fourth post-Minkowskian order (O(G^4)).
  • To include all velocity orders and radiative contributions, specifically the tail effect.
  • To utilize advanced scattering amplitude methods for gravitational dynamics.

Main Methods:

  • Generalized unitarity
  • The double copy technique
  • Multiloop integration methods
  • Effective field theory
  • Amplitude-action relation

Main Results:

  • The calculation of conservative two-body scattering dynamics at O(G^4) is completed.
  • Radiative contributions, including the tail effect, are incorporated.
  • The classical amplitude was found to involve complete elliptic integrals and polylogarithms.
  • The radial action was directly obtained from the amplitude.

Conclusions:

  • This work provides a significant advancement in the precision of gravitational dynamics calculations.
  • The methods used pave the way for future higher-order calculations in general relativity.
  • The results will improve the modeling of gravitational waveforms from compact object mergers.